Two capacitors of capacitances `C_1` and `C_2` are connected in parallel. If a charge Q is given to the combination, the ratio of the charge on the capacitor `C_2` to the charge on `C_2` will be :

Options

A. `(C_1)/(C_2)`
B. `sqrt((C_1)/(C_2))`
C. `sqrt((C_2)/(C_1))`
D. `(C_2)/(C_1)`

Answer

To solve the problem of finding the ratio of the charge on capacitor \( C_2 \) to the charge on capacitor \( C_1 \) when they are connected in parallel, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Configuration**:
- When capacitors are connected in parallel, they have the same potential difference across them. Therefore, the voltage \( V \) across both capacitors \( C_1 \) and \( C_2 \) is the same.

2. **Use the Formula for Charge on a Capacitor**:
- The charge \( Q \) on a capacitor is given by the formula:
\[ Q = C \times V \]
- For capacitor \( C_1 \), the charge \( Q_1 \) is:
\[ Q_1 = C_1 \times V \]
- For capacitor \( C_2 \), the charge \( Q_2 \) is:
\[ Q_2 = C_2 \times V \]

3. **Find the Ratio of Charges**:
- We need to find the ratio of the charge on capacitor \( C_2 \) to the charge on capacitor \( C_1 \):
\[ \text{Ratio} = \frac{Q_2}{Q_1} = \frac{C_2 \times V}{C_1 \times V} \]
- Since \( V \) is common in both the numerator and the denominator, it cancels out:
\[ \text{Ratio} = \frac{C_2}{C_1} \]

4. **Conclusion**:
- Therefore, the ratio of the charge on capacitor \( C_2 \) to the charge on capacitor \( C_1 \) is:
\[ \frac{Q_2}{Q_1} = \frac{C_2}{C_1} \]

### Final Answer:
The ratio of the charge on capacitor \( C_2 \) to the charge on capacitor \( C_1 \) is \( \frac{C_2}{C_1} \).

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